Fibonacci numbers

Description Each number in the Fibonacci sequence is the sum of its two predecessors, starting from 0 and 1. This simple description hides a wealth of ideas and applications, from the orderly arrangement of leaves on a plant to the chaos of Hamiltonian maps on a torus -- and with Penrose tilings somewhere between. There are links to musical and visual aesthetics, and even a stock-market application (allegedly). First you should survey the subject and explore the properties of Fibonacci numbers. After that you will be able to make a detailed study of one or more particular developments. This topic is suitable for several students. Prerequisites This is a topic which can be taken in many different directions. For many of these, you can start from 1H level maths. Resources Ron Knott's Fibonacci site is useful. This Encyclopedia article contains facts, references and lots of links. Ditto the Mathworld article. Wikipedia may provide some ideas. Here and here are sites devoted to the man himself. You could also look at his original book. Some books in the University Library. Here is a popular article about artistic connections. (In general with popular articles you should beware of rubbish, for example many of the sites here.)

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